# Definition:Inscribe

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## Definition

Let a geometric figure $A$ be constructed in the interior of another geometric figure $B$ such that:

Then $A$ is **inscribed** inside $B$.

### Circle in Polygon

A circle is **inscribed in** a polygon when it is tangent to each of the sides of that polygon:

### Polygon in Circle

A polygon is **inscribed in** a circle when each of its vertices lies on the circumference of the circle:

That is, the vertices are concyclic.

### Polygon in Polygon

A polygon is **inscribed in** another polygon when each of its vertices lies on the corresponding side of the other polygon.

### Polyhedron in Sphere

A polyhedron is **inscribed in** a sphere when each of its vertices lies on the surface of the sphere.

### Sphere in Polyhedron

A sphere is **inscribed in** a polyhedron when it is tangent to each of the faces of that polyhedron.

## Also see

- Results about
**inscribe**can be found**here**.

## Sources

- 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**inscribed** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**inscribed** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**inscribe**